Slide rule



Jan. 24, 1939. A. w. KEUFFEL SLIDE RULE Original Filed June 6, 1922 INVENTOR ADOLF 14 KEUFFEL Mad/11M ATTORNEYS Reisaued Jan. 24, 1939 UNITED STATES PATENT OFFICE SLIDE RULE Original No. 1,488,086, dated Apr-ll 1, 1924, Serial No. 566,340, June 8, 1922.

Application for reissue April 7, 1938, Serial No. 200,711

ZCIaims.

My invention relates to slide rules and more particularly to slide rules adapted for the solution of problems involving fractional powers and roots as well as natural or hyperbolic logarithms, and the novelty consists of the construction, adaptation and arrangement of the parts as will be more fully hereinafter pointed out.

The use of slide rules in many lines of business as well as professions has increased rapidly with the demand for quick and accurate solution of mathematical problems because the processes of business have changed, whereby instead of leaving the solution of such problems to the convenience of a corps of poorly paid clerks such problems are now solved immediately by the use of suitable slide rules adapted for the particular purpose required. This has resulted in the development and marketing of a large number of different types of slide rules adapted for many different purposes, but never has there been a slide rule especially adapted for figuring powers and roots of numbers less than unity whereby such problems may be solved directly on the rule.

My slide rule solves this problem and furnishes a means of solving problems involving numbers less than unity, directly, without the use of reciprocals.

Referring to the drawing: Figure 1 is a top plan view of my slide rule; and Figure 2 is a top plan view of the reverse side of my slide rule.

In the drawing bars H and J are rigidly secured together by means of plates K which are riveted thereto at M, so that a sliding bar N may be mounted between said bars H and J so as to be readily slidable longitudinally thereof. The slidable bar N has the usual tongue members on each edge adapted to slide in the usual groove members on the edges of the bars H and J contiguous to the sliding bar B so that the sliding bar N is always held in engagement between the bars H and J in whatever position it occupies longitudinally thereof. A runner or indicator X, transparent on both faces and of usual construction, is mounted over said bars H, J and N so as to be readily moved into any position desired between the plates K, and the runner X has a hair-line Y on each side thereof.

On the front of my slide rule as shown in Figure 1, the upper scale on the bar H is designated as LLB and has graduations representing the logarithms of co-logarithms 01' numbers less than unity, in the illustrated embodiment, from .05 to .97. The next scale on the bar H is designated as A and contains a double standard graduated logarithmic scale, The upper scale on the sliding bar N is designated as B, and has the same graduation as the scale A on the bar H. A second scale on the sliding bar N is designated as S, and has a graduated sine scale of degrees and minutes from 34 to and is used with 5 reference to scales A and B. The third scale on the sliding bar N is designated as T and has a graduated standard tangent scale with divisions from 5 43 to 45. The fourth scale on the sliding bar N is designated as C and has standard 10 graduated logarithmic divisions of full unit length from 1 to 10. The upper scale on the bar J is designated as LL3, and has graduations representing the logarithms of logarithms of the numbers from 2.7 to 22,000. The second scale on the 15 bar J is designated as LL2 and has graduations representing the logarithms of logarithms of the numbers from 1.105 to 2.7. The third scale on the bar J is designated as LLI, and has graduations representing the logarithms of logarithms 20 of the numbers from 1.01 to 1.105.

On the back of my slide rule, as shown in Figure 2, the scale shown on bar J is designated as DF, and is a standard logarithmic scale of full unit length the same as the C scale described above, except that it is folded and has its index at the centre. The upper scale on the sliding bar N is designated as CF, and is identical with the scale DF on bar J. The second scale on the sliding bar N is designated as CI and is a standard reciprocal logarithmic scale of full unit length graduated from 10 to l. The third scale on the sliding bar N is designated as C and is a standard logarthmic scale of full unit length identical with C scale above described. The first scale on the bar H is designated as D, and is the same as the scale C on the sliding bar N. The second scale on the bar H is designated as L and is a scale of equal parts from 0 to 1 and is used to obtain common logarithms when referred to scale D.

As has been above stated there have been slide rules on the market for some time, with which it is possible to solve problems involving fractional powers and roots as well as natural or hyperbolic logarithms. These slide rules of the prior art had graduated logarithmic scales designed as LLl, LL! and LLJ, the same as illustrated herein.

On these slides rules embodying the logarithmic scales mentioned it was not possible to handle, directly, roots and powers of numbers less than unity, as the reciprocal of the quantity must be first taken thereon, and this reciprocal then evaluated in the integral scales and then the reciprocal of the result taken in order to get the required answer. This operation involved a number of additional operations. both mentally and mechanically, and increased the liability of error, as the correctness of the result depended not on the mechanical operation of the slide rule alone, but also upon the mental operation of the operator combined with the mechanical operation 01' the slide rule.

My slide rule has overcome this difliculty and made it possible to handle roots and powers of numbers less than unity so as to obtain the solution of examples in formulae involving powers and roots of numbers less than unity directly on my slide rule by mere mechanical operation of the same and without the use of reciprocals of the quantities handled, thereby eliminating any separate mental operation and the possibility of errors involved therein.

In the equation of the catenary curve and in hyperbolic functions, the expression eoccurs in which e=2.7182+ is the base of natural or Napierian logarithms, also in many formulae the logarithms to the base e are required or is to be taken as a factor.

By placing the reciprocal of e on scale LLB in alignment with an index 1" of the regular logarithmic scale A, the values of e can be at once read for all values of :1: within the range of the scale, without the setting of the slide N and also the co-logarithms to base e can be directly read on A.

In order to make this clearer I will give a few examples, showing the old method as heretofore used and showing how to solve the problems by the new method.

Example 1 Required a:=0.8.

By the old method it is necessary to set the runner or indicator to .8 on scale C; read the reciprocal which is 1.25 on scale CI on the reverse side oi the rule, keep this number 1.25 in mind and then set the right index oi scale C to this number 1.25 on scale LLZ and opposite 5 on scale C read 3.05 on scale 1L3, now keep 3.05 in mind and then set runner to this number 3.05 on C; and read the reciprocal .328 on C1 which is the answer sought.

It will be noted that in this problem besides various operations of the slide and runner, it was necessary to take two readings mentally and reset the same on the slide rule, which may readily cause an error.

By my new method all that is necessary to solve the above example is to set the left index of scale B to 0.8 on scale LLU and opposite 5 on scale B read answer .328 on scale LLB.

Example 2 Required loge .635.

Old method-set runner to .635 on C; read reciprocal 1.575 on C1, keep this number in mind and set runner to 1.575 on LLZ; read .454 on D=logs 1.575. Taking the co-logarithm gives T546 as the answer. By the new method set the runner to .635 on scale LLll, read .454 on scale A, this is the co-logarlthm which deducted from 0 gives I546 as the answer.

What is claimed is:

1. In a slide rule a logarithmic scale and a scale representing logarithms of co-iogarithms of numbers less than unity, both of said scales being of the same suit length, whereby when the respective graduations on the scale representing logarithms of co-logarithms are in alignment with the graduations of the standard logarithmic scale representing the corresponding hyperbolic cologarithms, the hyperbolic co-logarithms oi numbers less than unity can be read directly from one to the other.

2. In a slide rule having relatively movable members, one logarithmic scale on one of said members, another identical logarithmic scale on another of said members and a scale representing logarithms of co-logarithms of numbers less than unity on one of said members, all three of said scales being to the same unit length whereby the hyperbolic co-logarithms of numbers less than unity can be multiplied or divided by any number of variables, the results being read as powers of said numbers on the scale representing logarithms of co-logarithms or as the hyperbolic logarithms thereof on the logarithmic scale on that member carrying the scale representing logarithms oi co-logarithms.

ADOLF W. KEUFFEL.

CERTIFICATE OF CORRECTION.

Reissue N0. 20,98h. January 2h, 1959.

ADOLF w. KIEUFFEL.

It is hereby certified that error appears in the printed specification of the above numbered patent requiring correction as follows: Page 2, second column, line 25, for "suit" read unit; and that the said Letters Patent should be read with this correction therein that the same may conform to the record of the case in the Patent Office.

Signed and sealed this lLLth day of March A. D. 1959.

Henry Van Arsdale (Seal) Acting Commissioner of Patents. 

